When a missile is fired from a ship, the probability that it is i…

MCQ

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

A
$\frac{1}{27}$
B
$\frac{3}{4}$
✓
$\frac{1}{8}$
D
$\frac{3}{8}$

✓

Answer

Correct option: C.

$\frac{1}{8}$

c
Required probability $=\left(\frac{2}{3} \times \frac{3}{4}\right)^{3}=\frac{1}{8}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If a matrix $A$ is such that $4{A^3} + 2{A^2} + 7A + I = O$, then ${A^{ - 1}}$ equals

→

If $y=y(x)$ and it follows the relation $4x{e^{xy}} = y + 5{\sin ^2}x$ ,then $y'(0)$ is equal to

→

Let the position vectors of the vertices $A , B$ and C of a triangle be $2 \hat{i}+2 \hat{j}+\hat{k}, \hat{i}+2 \hat{j}+2 \hat{k}$ and $2 \hat{ i }+\hat{ j }+2 \hat{ k }$ respectively. Let $l_1, l_2$ and $l_3$ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides $AB , BC$ and $CA$ respectively, then $l_1^2+l_2^2+l_3^2$ equals :

→

The number of points where the function

$f(x)=\left\{\begin{array}{clr}\left|2 x^{2}-3 x-7\right| \, \text { if } x \leq-1 \\ {\left[4 x^{2}-1\right]} \text { if } -1 < x < 1 \\ |x+1|+|x-2| \text { if } x \geq 1\end{array}\right.$

$[t]$ denotes the greatest integer $\leq t$, is discontinuous is

→

If a circle, whose centre is $(-1, 1)$ touches the straight line $x + 2y + 12 = 0$, then the coordinates of the point of contact are

→

If $\frac{d y}{d x}+\frac{2^{x-y}\left(2^{y}-1\right)}{2^{x}-1}=0, x, y>0, y(1)=1$, then $y (2)$ is equal to

→

Tangents $AB$ and $AC$ are drawn from the point $A(0,\,1)$ to the circle ${x^2} + {y^2} - 2x + 4y + 1 = 0$. Equation of the circle through $A, B$ and $C$ is

→

$\int {\frac{{{e^{{{\tan }^{ - 1}}\sqrt x }}}}{{\sqrt x + x\sqrt x }}dx = } $

→

In a $G.P.$ the sum of three numbers is $14$, if $1 $ is added to first two numbers and subtracted from third number, the series becomes $A.P.$, then the greatest number is

→